Can someone please help me with this??Find the equation for the following parabola ( Parabolas) !

The equation of the parabola is (x - 2)² = 16(y + 1) ⇒ D

Step-by-step explanation:

The standard form of the equation of the parabola is

(x - h)²  = 4p(y - k), where

∵ The vertex of the parabola is (2, -1)

→ By using the notes above

∴ h = 2

∴ k = -1

∵ Its focus is (2, 3)

→ By comparing it with the notes above

∴ h = 2

∴ k + p = 3

∵ k = -1

→ Substitute it in the equation above

∴ -1 + p = 3

→ Add 1 to both sides

∵ -1 + 1 + p = 3 + 1

∴ p = 4

→ Substitute the value of h, k, p in the form of the equation above

∵ (x - 2)² = 4(4)(y - -1)

→ Remember (-)(-) = (+)

∴ (x - 2)² = 16(y + 1)

∴ The equation of the parabola is (x - 2)² = 16(y + 1)

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get